The present invention concerns improved electromechanical filters with two or more real or complex poles. It is known (see the article by R. A. Johnson, published in the Proceedings of the IEEE Symposium on Circuits and Systems--Newton, April 1975) to realize poles in the transmission characteristic by disposing auxiliary couplers across non-adjacent resonators which are hereinafter referred to as bridges. The use of bridges has been summed up in the aforesaid publication as follows (Table 1 of the above article):
______________________________________ Resonators below length of bridge Phase Attenuation Pole Location bridge ______________________________________ EVEN -1:1 j.omega. Axis- Above & below passband 3.lambda./4 + p.lambda. EVEN +1:1 Complex- Right & Left 80 /4 + p.lambda. Half-planes ODD -1:1 j.omega. Axis- Below Filter passband 3.lambda./4 + p.lambda. ODD +1:1 j.omega. Axis- Above Filter passband 80 /4 + p.lambda. ______________________________________
where
n is a positive integer other than zero
p is a positive integer or zero, and
.lambda. is the wavelength at the central frequency of the filter in the vibration mode in which the bridge is operated.
As has been mentioned in the U.S. patent application Ser. No. 862,906 filed on Dec. 21, 1977 and now U.S. Pat. No. 4,163,960, assigned to the same Assignee as the present application for "Electromechanical filter structure", the bridge introduces into the passband variations of the transfer function which result in variations of amplitude in the transmitted band and undesirable modifications of the phase characteristic of the filter. It has been pointed out in the aforesaid application that these distortions decrease when the number of bridged resonators increases and are generally acceptable when this number reaches or exceeds four.
The present invention has essentially for its object to reduce the attenuation variations in the passband of a filter due to a bridge, and it is principally characterized in that the characteristics of the bridged cells are so designed that the image mobility of the bridged section is equal to that of the unbridged section.
In practice, where the number of bridged resonators is even, this condition can be met either through matching of the mobilities of the couplers of the bridged cells made of resonators identical over the whole structure, or using identical couplers for the bridged cells and modifying the mobility of the bridged resonators. Where the number of bridged resonators is odd, the condition affects the tuning frequencies of the bridged resonators and the mobility of one of the two parts of the bridged cells (either the coupler or the resonator).
The advantage of the improved filters according to the invention resides in their excellent performances in the passband with respect of both the attenuation and the phase. Experience has shown that the matching of the image mobilities of the bridged and unbridged sections provides correction of the attenuation, but also improves the phase characteristic in the transmitted band.